Research On Stability And Hopf Bifurcation Of Two Kinds Of Diffusion Neural Networks With Time Delay

The dynamic behavior of neural networks has broad development prospects in secure communication,image encryption and information technology,and other research fields.The research on its stability and bifurcation has always been a focus and focus of attention.As an important neural network model,the time-delayed diffusion neural network model has the characteristics of complex structure and dynamic richness,and its nonlinear dynamic behavior has gradually become a research hotspot for scholars.This paper mainly studied the stability and Hopf bifurcation of two types of delayed diffusion neural networks.The main contents and innovations of this article are as follows:(1)Stability and Hopf bifurcation of cellular neural network with time delay and diffusionFirst,a basic cell of cellular neural network is proposed,which is composed of two time-delayed Chua's circuits with the same lossless transmission line.Second,a kind of delayed diffusion cellular neural network is proposed,and its local stability condition and Hopf bifurcation behavior are analyzed.The proposed structure of cellular neural network is to interconnect adjacent cells by using linear resistance.Firstly,the equations describing cellular neural networks are transformed into two neutral differential equations with time delay by using the properties of discrete Laplacian operators.Then,taking the length of lossless transmission line as the bifurcation parameter,the stability and Hopf bifurcation behavior of the system are analyzed near the zero equilibrium point.Finally,the theory is verified by several simulations.(2)Hopf bifurcation and Turing instability of a reaction diffusion neutral neural network with time delayA two-dimensional diffusion neutral neural network with time delay is proposed.Firstly,under Neumann boundary condition,the condition of Turing instability is obtained.Some sufficient conditions for Hopf bifurcation are obtained by taking the time delay as the bifurcation parameter of the model.The direction and periodic solution of Hopf bifurcation are obtained by using the standard type theorem and central manifold theorem of partial differential equation.Finally,the theory is verified by several simulations.The results show that there are different spatiotemporal models near Turing instability point and Hopf bifurcation point,and the diffusion coefficient has a great influence on the model.